**Core Concept**
The question requires understanding of coagulation pathways and the role of specific factors in the prothrombin time (PT) and activated partial thromboplastin time (APTT) assays. PT measures the extrinsic and common pathways, while APTT measures the intrinsic and common pathways.

**Why the Correct Answer is Right**
The correct answer involves a condition where there is a deficiency in a factor that is common to both the intrinsic and extrinsic coagulation pathways. In this case, the factor is **Factor VII**, which is a key component of the extrinsic pathway, but also has a role in the common pathway. Deficiency or dysfunction of Factor VII would result in prolongation of both PT and APTT. This is because Factor VII is necessary for the generation of Factor X, which is a critical step in the common pathway.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is likely incorrect because it does not involve a common factor to both PT and APTT pathways. A deficiency in Factor VIII, for example, would only prolong APTT.
* **Option B:** This option is likely incorrect because it does not involve a condition that would affect both PT and APTT. A deficiency in Factor X, for example, would only prolong PT.
* **Option D:** This option is likely incorrect because it does not involve a condition that would affect both PT and APTT. A deficiency in Factor XII, for example, would only prolong APTT.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that both PT and APTT are prolonged in conditions involving a deficiency or dysfunction of a factor common to both pathways, such as Factor VII. This can help in diagnosing conditions like vitamin K deficiency or warfarin therapy.

**Correct Answer:** D. Factor XII deficiency.